A planar graph is one which has a plane embedding. Two drawings are **topologically isomorphic** if one can be continuously deformed into the other. If we wrap a drawing onto a sphere, and then off again, we can move any face to be the exterior face.

We know the following theorem.

**Theorem** (Whitney) **If $G$ is 3-connected, any two planar embeddings are equivalent.**

My question is as the title says.

**Is graph’s planar embedding unique if each block of one planar graph is 3-connected?**

Connectivity of the graph may even be one. I don’t know if there are any counterexamples or it may be true. Not sure if this is a proven fact.

**PS:** A **block** of a graph G is a maximal subgraph which is either an isolated vertex, a bridge edge, or a 2-connected subgraph.